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Talk:N primitive
N primitive vs. Y sequence Which version of N primitive is stronger than Y sequence? Has anyone compared them? {hyp/^,cos} (talk) 11:58, November 18, 2019 (UTC) : Nayuta did, but after that I think that it turned out to be dead. I guess that it means that the analysis contained an unexpected error. I am not certain which version it was. At least, there are no valid analysis against the limit of Y sequence, because there are several standard expressions whose expansions are kept undefined. As far as I know, N primitive is the only example of difference sequence systems in Japanese googology which has been formalised beyond the standard expression which is expected to correspond to the limit of BM2.3. : p-adic 12:31, November 18, 2019 (UTC) ::> N primitive is the only example of difference sequence systems in Japanese googology which has been formalised beyond the standard expression which is expected to correspond to the limit of BM2.3. ::Isn't Y sequence formalized yet? --Nayuta Ito (talk) 02:43, November 19, 2019 (UTC) ::: Not yet. Yukito has not defined even the subsystem below (1,3), because the issue on his original definition is irrelevant to the size. There are several alternative definitions by me, koteitan, Hexirp, and Syst3ms, but they are not official definitions. Yukito can decide to choose one of them, and also to define it by himself. ::: p-adic 02:54, November 19, 2019 (UTC) Differences What is the differences between versions of N primitive? Sources are not in usual English. {hyp/^,cos} (talk) 03:32, November 19, 2019 (UTC) : The main difference between Nn and Nn½ is that the latter one use expressions which include ½ in their entries. It is evaluated like 0.5 in the usual sense. Since we have 1 < 1.5 < 2, the use of ½ allows us to consider intermediate values, which help us to expand in a way more similar to BM2.3. Namely, Nn½ restricted to standard expressions below (0,1,3) is more similar to BM2.3. Another difference between two versions is the way to fill entries of the expanded sequence which are not copies of ancestors of the rightmost entry of the original sequence. In order to avoid an unexpected occurrence of "changing the parent-child relation" in expansions, we need to carefully define how to ascend such non-Ancestor entries. Also, there seems a difference in the way to define BadRoot. Of course, all of N primitive are intended to be extensions of primitive sequence system, and hence the difference is not intended to occur for standard expressions below (0,1,2,4). We are not certain which version is the strongest under the assumption of the termination. : p-adic 03:57, November 19, 2019 (UTC) What's the corresponding ordinal of these N primitive sequences? \( (0,1,2,4,5) \) \( (0,1,2,4,5,5) \) \( (0,1,2,4,5,6) \) \( (0,1,2,4,5,7) \) \( (0,1,2,4,6) \) \( (0,1,2,4,6,6) \) \( (0,1,2,4,6,7) \) \( (0,1,2,4,6,8) \) \( (0,1,2,4,6,9) \) \( (0,1,2,4,7) \) \( (0,1,2,4,7,7) \) \( (0,1,2,4,7,8) \) \( (0,1,2,4,7,9) \) \( (0,1,2,4,7,10) \) \( (0,1,2,4,7,11) \) \( (0,1,2,4,8) \) \( (0,1,2,4,8,8) \) \( (0,1,2,4,8,9) \) \( (0,1,2,4,8,10) \) \( (0,1,2,4,8,11) \) \( (0,1,2,4,8,12) \) \( (0,1,2,4,8,13) \) \( (0,1,2,4,8,14) \) \( (0,1,2,4,8,15) \) \( (0,1,2,4,8,16) \) Qq1010903229 (talk) 02:20, December 14, 2019 (UTC) : The following is my guess without any proof besed on unreasonable pattern matching. \begin{eqnarray*} (0,1,2,4,5) & \mapsto & \psi_0(\psi_1(\psi_0(0))) \\ (0,1,2,4,5,5) & \mapsto & \psi_0(\psi_1(\psi_0(0)+\psi_0(0))) \\ (0,1,2,4,5,6) & \mapsto & \psi_0(\psi_1(\psi_0(\psi_0(0)))) \\ (0,1,2,4,5,7) & \mapsto & \psi_0(\psi_1(\psi_0(\psi_1(0)))) \\ (0,1,2,4,6) & \mapsto & \psi_0(\psi_1(\psi_1(0))) \\ (0,1,2,4,6,6) & \mapsto & \psi_0(\psi_1(\psi_1(0)+\psi_1(0))) \\ (0,1,2,4,6,7) & \mapsto & \psi_0(\psi_1(\psi_1(\psi_0(0))) \\ (0,1,2,4,6,8) & \mapsto & \psi_0(\psi_1(\psi_1(\psi_1(0)))) \\ (0,1,2,4,6,9) & \mapsto & \psi_0(\psi_2(0)) \\ (0,1,2,4,7) & \mapsto & \psi_0(\psi_{\omega}(0)) \\ (0,1,2,4,7,7) & \mapsto & \psi_0(\psi_{\omega}(0)+\psi_{\omega}(0)) \\ (0,1,2,4,7,8) & \mapsto & \psi_0(\psi_{\omega}(\psi_0(0))) \\ (0,1,2,4,7,9) & \mapsto & \psi_0(\psi_{\omega}(\psi_1(0))) \\ (0,1,2,4,7,10) & \mapsto & \psi_0(\psi_{\omega}(\psi_{\omega}(0))) \\ (0,1,2,4,7,11) & \mapsto & \psi_0(\psi_{\omega^2}(0)) \\ (0,1,2,4,8) & \mapsto & \textrm{Nobody knows,} \end{eqnarray*} : where \(\psi\) denotes extended Buchholz's OCF. I note that it is difficult to verify the correspondence even when we work with pair sequence system, as nobody could verify the termination of it before I wrote the proof. In particular, nobody has analysed N primitive using ordinals in that realm. (Analyses of BMS and its variant are just "guesses" based on no theoretic reason. Moreover, many of them are described by UNOCF, which is known to be ill-defined.) : p-adic 06:09, December 14, 2019 (UTC)